RUN: FILE NAMES FILE PROCESSED: run_me DATA FILE PROCESSED: fran019l.rwl LOG FILE PROCESSED: fran019l.rwl_log OPTION PLOT TREE-RING DATA TYPE 1 !TUCSON RING-WIDTH FORMAT MISSING DATA IN GAPS -9 0 !MISSING VALUES ESTIMATED (NO PLOTS) DATA TRANSFORMATION 0 0 !NO DATA TRANSFORMATION (NO PLOTS) FIRST DETRENDING 1 0 !1ST-NEG EXPONENTIAL CURVE, NO = OPT 3 SECOND DETRENDING -67 0 !2ND-SPLINE CURVE (PCT N 50% CUTOFF) ROBUST DETRENDING 1 !NON-ROBUST DETRENDING METHODS USED INTERACTIVE DETREND 0 !NO INTERACTIVE DETRENDING INDEX CALCULATION 1 !TREE-RING INDICES OR RATIOS (Rt/Gt) AR MODELING METHOD 1 0 !NON-ROBUST AUTOREGRESSIVE MODELING POOLED AR ORDER 0 0 !MINIMUM AIC POOLED AR MODEL ORDER FIT SERIES AR ORDER 0 !POOLED AR ORDER FIT TO ALL SERIES MEAN CHRONOLOGY 2 0 !ROBUST CHRONOLOGY (NO BIWEIGHT PLOTS) STABILIZE VARIANCE 1 !RBAR WEIGHTED STABILIZATION METHOD COMMON PERIOD YEARS 0 0 !NO COMMON PERIOD ANALYSIS PERFORMED SITE-TREE-CORE MASK SSSTTCC !SITE-TREE-CORE SEPARATION MASK RUNNING RBAR 50 25 0 !RUNNING RBAR WINDOW/OVERLAP (NO PLOTS) PRINTOUT OPTION 2 !SUMMARY & SERIES STATISTICS PRINTED CORE SERIES SAVE 1 !SERIES SAVED IN TUCSON RAW DATA FORMAT SUMMARY PLOT DISPLAYS 0 !NO SPAGHETTI AND MEAN CHRONOLOGY PLOTS STAND DYNAMICS ANALYSES 0 !NO STAND DYNAMICS ANALYSES DONE RUNNING MEAN WINDOW WIDTH 0 !RUNNING MEAN WINDOW WIDTH PERCENT GROWTH CHANGE 0 !PERCENT GROWTH CHANGE THRESHOLD STANDARD ERROR THRESHOLD 0 !STANDARD ERROR LIMIT THRESHOLD |======================== RAW DATA STATISTICAL ANALYSES =======================| |------------------- TREE-RING SERIES READ IN FOR PROCESSING ------------------| DATA HEADER LINES: 264 1 Mt.Cenis WIDTH_LATE PCAB - 264 2 France Norway spruce 1950 4516-655 1834 1975 - 264 3 FRITZ SCHWEINGRUBER - |------------ SERIES GAPS FOUND BASED ON ANY NEGATIVE NUMBER FOUND ------------| SERIES IDENT RESULTS OF SCANS FOR GAPS OR MISSING VALUES 7 264090 MISSING VALUES FOUND: 9 IN 1 GAPS / 1905 1913 / -------------------------------------------------------------------- |------------------ STATISTICS OF RAW TREE-RING MEASUREMENTS ------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 264010 1876 1975 100 0.295 0.108 0.689 3.213 0.296 0.490 2 264020 1839 1975 137 0.232 0.128 1.738 5.505 0.275 0.784 3 264030 1859 1975 117 0.263 0.114 0.465 3.083 0.312 0.609 4 264040 1864 1975 112 0.168 0.063 0.744 4.309 0.299 0.429 5 264070 1834 1975 142 0.263 0.097 0.593 3.677 0.283 0.532 6 264080 1884 1975 92 0.269 0.127 1.557 5.795 0.312 0.522 7 264090 1866 1975 110 0.371 0.159 0.650 2.923 0.266 0.655 8 264110 1853 1975 123 0.206 0.117 1.388 5.452 0.362 0.633 9 264160 1869 1975 107 0.300 0.146 1.968 8.739 0.364 0.463 10 264190 1853 1975 123 0.275 0.108 0.436 2.801 0.320 0.511 11 264200 1869 1975 107 0.370 0.140 0.086 2.445 0.328 0.421 12 264220 1864 1975 112 0.269 0.110 1.237 5.726 0.312 0.544 NUMBER OF SERIES READ IN: 12 FROM 1834 TO 1975 142 YEARS |---------------- SUMMARY OF RAW TREE-RING SERIES STATISTICS ------------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 114 0.273 0.118 0.963 4.472 0.311 0.549 STANDARD DEVIATION 14 0.058 0.025 0.593 1.835 0.030 0.105 MEDIAN (50TH QUANTILE) 112 0.269 0.116 0.716 3.993 0.312 0.527 INTERQUARTILE RANGE 19 0.050 0.026 0.943 2.613 0.034 0.144 MINIMUM VALUE 92 0.168 0.063 0.086 2.445 0.266 0.421 LOWER HINGE (25TH QUANTILE) 104 0.247 0.108 0.529 3.003 0.290 0.477 UPPER HINGE (75TH QUANTILE) 123 0.297 0.134 1.472 5.616 0.324 0.621 MAXIMUM VALUE 142 0.371 0.159 1.968 8.739 0.364 0.784 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 66 0.302 0.260 0.032 -0.237 1.911 -0.171 0.716 MINIMUM CORRELATION: -0.171 SERIES 264090 AND 264160 107 YEARS MAXIMUM CORRELATION: 0.716 SERIES 264030 AND 264040 112 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 75.26 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1890. 1915. 1940. CORR 21. 66. 66. RBAR 0.366 0.393 0.282 SDEV 0.169 0.172 0.275 SERR 0.037 0.021 0.034 EPS 0.866 0.886 0.825 NSS 11.2 12.0 12.0 |======================== RAW DATA CHRONOLOGY STATISTICS ======================| |----------------- ROBUST MEAN RAW DATA CHRONOLOGY STATISTICS -----------------| FIRST LAST TOTAL MEAN STDRD SKEW KURTOSIS MEAN SERIAL YEAR YEAR YEARS INDEX DEV COEFF COEFF SENS CORR 1834 1975 142 0.277 0.088 0.495 2.873 0.242 0.541 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.578 0.310 0.019 52 90 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.51 2.26 1.01 1.11 3.37 34.10 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.92 0.16 0.00 0.84 1.00 1.00 |--------------------- SEGMENT LENGTH SUMMARY STATISTICS ----------------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LENGTH RANGE LENGTH HINGE HINGE LENGTH 112. 16. 92. 107. 123. 142. |----------- RAW DATA CHRONOLOGY AUTO AND PARTIAL AUTOCORRELATIONS ------------| LAG T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 ACF 0.537 0.519 0.487 0.459 0.401 0.392 0.439 0.290 0.335 0.316 PACF 0.537 0.324 0.195 0.125 0.029 0.056 0.158 -0.131 0.047 0.033 95% C.L. 0.168 0.211 0.244 0.270 0.291 0.306 0.320 0.337 0.344 0.353 |------------------ RAW DATA CHRONOLOGY AUTOREGRESSIVE MODEL ------------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 4 0.428 0.244 0.234 0.175 0.153 |================== DETRENDED DATA CURVE FITS AND STATISTICS ==================| |------------------------ RESULTS OF FIRST DETRENDING -------------------------| |--------------- GROWTH CURVE USED FOR DETRENDING TREE-RING DATA --------------| CURVE OPTION -2: REGIONAL CURVE DETRENDING F(I) = ONE AGE-ALIGNED CURVE CURVE OPTION -1: FIRST-DIFFERENCES F(I) = Y(I) - Y(I-1) CURVE OPTION 1: NEG EXPON CURVE, NO = OPT 3 F(I) = A*EXP(-B*T(I)) + D CURVE OPTION 2: NEG EXPON CURVE, NO = OPT 4 F(I) = A*EXP(-B*T(I)) + D CURVE OPTION 3: LINEAR REGRESSION (ANY SLOPE) F(I) = +/-C*T(I) + D CURVE OPTION 4: LINEAR REGRESSION (NEG SLOPE) F(I) = -C*T(I) + D CURVE OPTION 5: HORIZONTAL LINE THROUGH MEAN F(I) = MEAN(Y(I)) = D CURVE OPTION 6: HUGERSHOFF GROWTH FUNCTION F(I) = A*T(I)**B * EXP(C*T(I)) CURVE OPTION 7: GENERAL EXPONENTIAL CURVE F(I) = A*T(I) * EXP(-B*T(I)) CURVE OPTION >9: CUBIC SMOOTHING SPLINE FIXED 50 PCT VARIANCE CUTOFF CURVE OPTION <-9: CUBIC SMOOTHING SPLINE PCT N 50 PCT VARIANCE CUTOFF SERIES IDENT OPTION A B C D 1 264010 3 0.00000000 0.00000000 -0.00052703 0.32111517 2 264020 1 0.52306235 0.05310751 0.00000000 0.16238622 3 264030 3 0.00000000 0.00000000 -0.00217686 0.39125553 4 264040 3 0.00000000 0.00000000 -0.00086104 0.21632722 5 264070 3 0.00000000 0.00000000 -0.00135608 0.35956547 6 264080 3 0.00000000 0.00000000 -0.00027010 0.28179884 7 264090 3 0.00000000 0.00000000 -0.00178662 0.48692772 8 264110 1 0.26789233 0.02365300 0.00000000 0.12014626 9 264160 3 0.00000000 0.00000000 0.00138228 0.22507671 10 264190 3 0.00000000 0.00000000 0.00129097 0.19516326 11 264200 3 0.00000000 0.00000000 -0.00219734 0.48828247 12 264220 3 0.00000000 0.00000000 -0.00222909 0.39513996 |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 264010 1876 1975 100 1.000 0.362 0.641 2.952 0.293 0.477 2 264020 1839 1975 137 1.000 0.272 0.510 3.609 0.274 0.194 3 264030 1859 1975 117 0.994 0.334 0.506 3.170 0.310 0.361 4 264040 1864 1975 112 0.999 0.333 0.733 4.301 0.297 0.335 5 264070 1834 1975 142 0.997 0.295 0.418 4.180 0.282 0.300 6 264080 1884 1975 92 1.000 0.475 1.678 6.323 0.308 0.525 7 264090 1866 1975 110 0.994 0.402 0.568 2.590 0.273 0.623 8 264110 1853 1975 123 0.999 0.438 0.741 3.638 0.359 0.473 9 264160 1869 1975 107 1.003 0.450 1.296 5.690 0.361 0.408 10 264190 1853 1975 123 1.000 0.364 0.613 3.564 0.318 0.404 11 264200 1869 1975 107 0.996 0.344 0.562 3.544 0.325 0.347 12 264220 1864 1975 112 1.002 0.291 0.836 6.254 0.310 0.179 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 115 0.999 0.363 0.758 4.151 0.309 0.385 STANDARD DEVIATION 14 0.003 0.066 0.368 1.266 0.029 0.129 MEDIAN (50TH QUANTILE) 112 0.999 0.353 0.627 3.624 0.309 0.382 INTERQUARTILE RANGE 16 0.004 0.106 0.253 1.639 0.034 0.158 MINIMUM VALUE 92 0.994 0.272 0.418 2.590 0.273 0.179 LOWER HINGE (25TH QUANTILE) 107 0.996 0.314 0.536 3.357 0.288 0.317 UPPER HINGE (75TH QUANTILE) 123 1.000 0.420 0.789 4.996 0.321 0.475 MAXIMUM VALUE 142 1.003 0.475 1.678 6.323 0.361 0.623 |------------------------ RESULTS OF SECOND DETRENDING ------------------------| |--------------- GROWTH CURVE USED FOR DETRENDING TREE-RING DATA --------------| CURVE OPTION -2: REGIONAL CURVE DETRENDING F(I) = ONE AGE-ALIGNED CURVE CURVE OPTION -1: FIRST-DIFFERENCES F(I) = Y(I) - Y(I-1) CURVE OPTION 1: NEG EXPON CURVE, NO = OPT 3 F(I) = A*EXP(-B*T(I)) + D CURVE OPTION 2: NEG EXPON CURVE, NO = OPT 4 F(I) = A*EXP(-B*T(I)) + D CURVE OPTION 3: LINEAR REGRESSION (ANY SLOPE) F(I) = +/-C*T(I) + D CURVE OPTION 4: LINEAR REGRESSION (NEG SLOPE) F(I) = -C*T(I) + D CURVE OPTION 5: HORIZONTAL LINE THROUGH MEAN F(I) = MEAN(Y(I)) = D CURVE OPTION 6: HUGERSHOFF GROWTH FUNCTION F(I) = A*T(I)**B * EXP(C*T(I)) CURVE OPTION 7: GENERAL EXPONENTIAL CURVE F(I) = A*T(I) * EXP(-B*T(I)) CURVE OPTION >9: CUBIC SMOOTHING SPLINE FIXED 50 PCT VARIANCE CUTOFF CURVE OPTION <-9: CUBIC SMOOTHING SPLINE PCT N 50 PCT VARIANCE CUTOFF SERIES IDENT OPTION A B C D 1 264010 -67 67 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 2 264020 -67 91 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 3 264030 -67 78 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 4 264040 -67 75 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 5 264070 -67 95 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 6 264080 -67 61 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 7 264090 -67 73 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 8 264110 -67 82 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 9 264160 -67 71 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 10 264190 -67 82 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 11 264200 -67 71 SMOOTHING SPLINE CURVE AND WINDOW WIDTH 12 264220 -67 75 SMOOTHING SPLINE CURVE AND WINDOW WIDTH |-------------------- STATISTICS OF SINGLE TREE-RING SERIES -------------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 264010 1876 1975 100 0.997 0.305 0.459 3.235 0.294 0.309 2 264020 1839 1975 137 1.000 0.271 0.526 3.634 0.274 0.188 3 264030 1859 1975 117 0.996 0.298 0.223 3.062 0.310 0.206 4 264040 1864 1975 112 0.997 0.319 0.813 5.200 0.297 0.299 5 264070 1834 1975 142 0.999 0.282 0.213 4.143 0.282 0.219 6 264080 1884 1975 92 0.983 0.390 1.367 5.141 0.306 0.386 7 264090 1866 1975 110 0.996 0.257 0.148 2.944 0.273 0.205 8 264110 1853 1975 123 0.995 0.417 0.569 3.173 0.359 0.449 9 264160 1869 1975 107 0.994 0.391 1.312 6.981 0.361 0.285 10 264190 1853 1975 123 0.993 0.310 0.004 2.916 0.317 0.219 11 264200 1869 1975 107 0.995 0.281 0.114 3.362 0.326 0.078 12 264220 1864 1975 112 0.998 0.279 0.688 6.124 0.310 0.132 |---------------- SUMMARY OF SINGLE TREE-RING SERIES STATISTICS ---------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 115 0.995 0.317 0.536 4.160 0.309 0.248 STANDARD DEVIATION 14 0.004 0.053 0.449 1.376 0.029 0.104 MEDIAN (50TH QUANTILE) 112 0.996 0.302 0.492 3.498 0.308 0.219 INTERQUARTILE RANGE 16 0.003 0.074 0.570 2.053 0.034 0.107 MINIMUM VALUE 92 0.983 0.257 0.004 2.916 0.273 0.078 LOWER HINGE (25TH QUANTILE) 107 0.994 0.280 0.181 3.118 0.288 0.197 UPPER HINGE (75TH QUANTILE) 123 0.998 0.354 0.751 5.170 0.322 0.304 MAXIMUM VALUE 142 1.000 0.417 1.367 6.981 0.361 0.449 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 66 0.351 0.134 0.017 -0.747 4.090 -0.097 0.578 MINIMUM CORRELATION: -0.097 SERIES 264080 AND 264110 92 YEARS MAXIMUM CORRELATION: 0.578 SERIES 264030 AND 264040 112 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 75.26 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1890. 1915. 1940. CORR 21. 66. 66. RBAR 0.417 0.398 0.330 SDEV 0.137 0.156 0.199 SERR 0.030 0.019 0.024 EPS 0.889 0.888 0.855 NSS 11.2 12.0 12.0 |======================== STANDARD CHRONOLOGY STATISTICS ======================| *** VARIANCE STABILIZED WITH BRIFFA RBAR-WEIGHTED METHOD *** |----------------- ROBUST MEAN STANDARD CHRONOLOGY STATISTICS -----------------| FIRST LAST TOTAL MEAN STDRD SKEW KURTOSIS MEAN SERIAL YEAR YEAR YEARS INDEX DEV COEFF COEFF SENS CORR 1834 1975 142 0.985 0.201 -0.255 3.508 0.232 0.021 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.262 0.124 0.085 37 105 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.56 1.79 1.02 1.17 2.96 5.68 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.89 0.13 0.00 0.85 0.98 1.00 |----------- STANDARD CHRONOLOGY AUTO AND PARTIAL AUTOCORRELATIONS ------------| LAG T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 ACF 0.021 0.029 -0.071 -0.125 -0.106 -0.064 0.040 -0.211 -0.027 -0.035 PACF 0.021 0.029 -0.072 -0.123 -0.100 -0.061 0.029 -0.246 -0.069 -0.056 95% C.L. 0.168 0.168 0.168 0.169 0.171 0.173 0.174 0.174 0.181 0.181 |------------------ STANDARD CHRONOLOGY AUTOREGRESSIVE MODEL ------------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 0 0.000 |======================= POOLED AUTOREGRESSION ANALYSIS =======================| POOLED AUTOCORRELATIONS: LAG T= -1 T= -2 T= -3 T= -4 T= -5 T= -6 T= -7 T= -8 T= -9 T=-10 -0.018 0.061 -0.094 -0.175 -0.037 -0.054 0.081 -0.241 0.037 -0.041 YULE-WALKER ESTIMATES OF AUTOREGRESSION: ORDER T= -1 T= -2 T= -3 T= -4 T= -5 T= -6 T= -7 T= -8 T= -9 T=-10 1 -0.018 2 -0.017 0.061 3 -0.011 0.059 -0.093 4 -0.028 0.070 -0.095 -0.183 5 -0.034 0.067 -0.092 -0.184 -0.034 6 -0.036 0.059 -0.096 -0.181 -0.035 -0.044 7 -0.034 0.061 -0.087 -0.176 -0.038 -0.042 0.051 8 -0.019 0.049 -0.098 -0.226 -0.063 -0.025 0.042 -0.284 9 -0.021 0.049 -0.098 -0.227 -0.065 -0.025 0.042 -0.284 -0.007 10 -0.021 0.043 -0.097 -0.227 -0.066 -0.030 0.040 -0.283 -0.007 -0.021 LAST TERM IN EACH ROW ABOVE EQUALS THE PARTIAL AUTOCORRELATION COEFFICIENT AKAIKE INFORMATION CRITERION: AR( 0) AR( 1) AR( 2) AR( 3) AR( 4) AR( 5) 915.23 917.19 918.66 919.44 916.59 918.42 AR( 6) AR( 7) AR( 8) AR( 9) AR(10) 920.15 921.78 911.86 913.86 915.79 SELECTED AUTOREGRESSION ORDER: 8 AR ORDER SELECTION CRITERION: IPP=0 FIRST-MINIMUM AIC SELECTION THE AIC TRACE SHOULD BE CHECKED TO SEE IF AR ORDER SELECTION CRITERION IS ADEQUATE. E.G. IF AR-ORDERS OF THE FIRST-MINIMUM AND THE FULL-MINIMUM AIC ARE CLOSE, AN ARSTAN RUN WITH FULL-MINIMUM AIC ORDER SELECTION MIGHT BE TRIED AUTOREGRESSION COEFFICIENTS: T= -1 T= -2 T= -3 T= -4 T= -5 T= -6 T= -7 T= -8 T= -9 T=-10 -0.019 0.049 -0.098 -0.226 -0.063 -0.025 0.042 -0.284 R-SQUARED DUE TO POOLED AUTOREGRESSION: 12.75 PCT VARIANCE INFLATION FROM AUTOREGRESSION: 114.61 PCT IMPULSE RESPONSE FUNCTION WEIGHTS FOR THIS AR ( 8) PROCESS OUT TO ORDER 50: 1.0000 -0.019 0.049 -0.100 -0.220 -0.064 -0.034 0.081 -0.226 0.050 -.0208 0.029 0.100 0.019 0.022 -0.048 0.042 -0.032 0.006 -0.001 -.0313 0.001 -0.010 0.019 -0.007 0.013 -0.001 -0.003 0.008 -0.004 0.0041 -0.006 0.002 -0.004 0.000 0.002 -0.002 0.002 -0.002 0.002 -.0006 0.001 0.000 -0.001 0.001 -0.001 0.001 0.000 0.000 0.000 |================== INDIVIDUAL SERIES AUTOREGRESSION ANALYSES =================| |---------------- INDIVIDUAL SERIES AUTOREGRESSIVE COEFFICIENTS ---------------| SERIES IDENT ORDER RSQ t-1 t-2 t-3 ..... t-IP 1 264010 8 0.165 0.271 0.133 -0.041 -0.143 -0.008 0.014 0.004 -0.192 2 264020 8 0.074 0.162 0.163 -0.029 -0.031 -0.055 0.018 0.012 -0.098 3 264030 8 0.113 0.181 0.117 -0.034 -0.066 0.043 0.111 -0.015 -0.229 4 264040 8 0.231 0.282 0.141 0.027 -0.169 -0.048 0.184 0.092 -0.316 5 264070 8 0.139 0.211 -0.011 0.041 -0.108 -0.129 0.050 0.002 -0.233 6 264080 8 0.301 0.277 0.155 0.323 -0.059 -0.078 -0.071 0.142 -0.144 7 264090 8 0.110 0.187 0.147 -0.058 -0.046 0.120 -0.159 -0.056 -0.044 8 264110 8 0.271 0.474 0.049 -0.070 0.033 0.043 -0.157 0.234 -0.205 9 264160 8 0.162 0.262 0.199 -0.145 0.091 0.150 -0.106 0.024 -0.068 10 264190 8 0.116 0.205 0.009 0.052 0.049 0.158 -0.068 -0.025 -0.077 11 264200 8 0.155 0.084 0.140 -0.062 -0.281 0.046 -0.058 0.041 -0.173 12 264220 8 0.114 0.088 0.241 0.034 -0.027 -0.003 0.014 -0.006 -0.193 |------------- SUMMARY STATISTICS FOR AUTOREGRESSIVE COEFFICIENTS -------------| ORDER RSQ t-1 t-2 t-3 ..... t-IP ARITHMETIC MEAN 8 0.162 0.224 0.124 0.003 -0.063 0.020 -0.019 0.038 -0.164 STANDARD DEVIATION 0 0.070 0.104 0.074 0.116 0.102 0.091 0.104 0.081 0.081 MEDIAN 8 0.147 0.208 0.140 -0.032 -0.053 0.020 -0.022 0.008 -0.183 INTERQUARTILE RANGE 0 0.084 0.102 0.076 0.097 0.128 0.135 0.123 0.077 0.130 MINIMUM VALUE 8 0.074 0.084 -0.011 -0.145 -0.281 -0.129 -0.159 -0.056 -0.316 LOWER HINGE 8 0.113 0.172 0.083 -0.060 -0.125 -0.052 -0.089 -0.010 -0.217 UPPER HINGE 8 0.198 0.274 0.159 0.037 0.003 0.083 0.034 0.067 -0.087 MAXIMUM VALUE 8 0.301 0.474 0.241 0.323 0.091 0.158 0.184 0.234 -0.044 |------------------- STATISTICS OF PREWHITENED TREE-RING DATA -----------------| SERIES IDENT FRST LAST YEAR MEAN STDEV SKEW KURT SENS AC(1) 1 264010 1876 1975 100 1.000 0.278 0.178 2.599 0.329 -0.004 2 264020 1839 1975 137 1.000 0.261 0.441 3.569 0.293 -0.003 3 264030 1859 1975 117 1.000 0.280 -0.011 3.270 0.328 0.000 4 264040 1864 1975 112 1.000 0.278 0.527 5.099 0.321 -0.038 5 264070 1834 1975 142 1.000 0.262 -0.337 4.276 0.300 0.009 6 264080 1884 1975 92 1.000 0.325 1.082 4.691 0.337 0.011 7 264090 1866 1975 110 1.000 0.242 -0.204 3.582 0.292 -0.002 8 264110 1853 1975 123 1.000 0.354 0.787 4.081 0.405 0.004 9 264160 1869 1975 107 1.000 0.359 0.698 5.108 0.414 0.000 10 264190 1853 1975 123 1.000 0.296 -0.275 3.279 0.334 0.011 11 264200 1869 1975 107 1.000 0.262 0.174 3.376 0.307 0.029 12 264220 1864 1975 112 1.000 0.263 0.523 5.073 0.301 0.002 |------------- SUMMARY OF PREWHITENED TREE-RING SERIES STATISTICS -------------| YEAR MEAN STDEV SKEW KURT SENS AC(1) ARITHMETIC MEAN 115 1.000 0.288 0.299 4.000 0.330 0.002 STANDARD DEVIATION 14 0.000 0.038 0.452 0.848 0.040 0.016 MEDIAN (50TH QUANTILE) 112 1.000 0.278 0.309 3.831 0.324 0.001 INTERQUARTILE RANGE 16 0.000 0.048 0.720 1.554 0.035 0.012 MINIMUM VALUE 92 1.000 0.242 -0.337 2.599 0.292 -0.038 LOWER HINGE (25TH QUANTILE) 107 1.000 0.262 -0.107 3.327 0.301 -0.002 UPPER HINGE (75TH QUANTILE) 123 1.000 0.310 0.612 4.882 0.336 0.010 MAXIMUM VALUE 142 1.000 0.359 1.082 5.108 0.414 0.029 |-------------------- ALL POSSIBLE SERIES RBAR STATISTICS ---------------------| TOTAL MEAN STANDARD STANDARD SKEWESS KURTOSIS MINIMUM MAXIMUM CORRS RBAR DEVIATION ERROR COEFF COEFF CORR CORR 66 0.381 0.111 0.014 -0.540 3.900 0.001 0.600 MINIMUM CORRELATION: 0.001 SERIES 264080 AND 264110 92 YEARS MAXIMUM CORRELATION: 0.600 SERIES 264010 AND 264090 100 YEARS PERCENT OF ALL POSSIBLE CORRELATIONS USED (N>20 YEARS): 100.00 PERCENT OF ALL POSSIBLE TREE-RING YEARS USED IN RBAR: 75.26 |--------------------------- RUNNING RBAR STATISTICS --------------------------| YEAR 1890. 1915. 1940. CORR 21. 66. 66. RBAR 0.425 0.423 0.344 SDEV 0.124 0.140 0.154 SERR 0.027 0.017 0.019 EPS 0.893 0.898 0.863 NSS 11.2 12.0 12.0 |======================== RESIDUAL CHRONOLOGY STATISTICS ======================| *** VARIANCE STABILIZED WITH BRIFFA RBAR-WEIGHTED METHOD *** |----------------- ROBUST MEAN RESIDUAL CHRONOLOGY STATISTICS -----------------| FIRST LAST TOTAL MEAN STDRD SKEW KURTOSIS MEAN SERIAL YEAR YEAR YEARS INDEX DEV COEFF COEFF SENS CORR 1834 1975 142 0.991 0.192 -0.498 3.723 0.242 -0.161 MEAN INDICES VS THEIR STANDARD DEVIATIONS ROBUST MEAN EFFICIENCY RESULTS CORRELATION SLOPE INTERCEPT # IMPROVED # UNIMPROVED 0.178 0.078 0.113 35 107 |---------------- ROBUST MEAN EFFICIENCY GAIN AND LOSS RESULTS ----------------| MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM GAIN RANGE GAIN HINGE HINGE GAIN 1.34 1.16 1.00 1.11 2.27 5.49 MEDIAN INTERQUARTILE MINIMUM LOWER UPPER MAXIMUM LOSS RANGE LOSS HINGE HINGE LOSS 0.88 0.13 0.00 0.85 0.98 1.00 |----------- RESIDUAL CHRONOLOGY AUTO AND PARTIAL AUTOCORRELATIONS ------------| LAG T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 ACF -0.160 -0.057 -0.074 -0.034 -0.102 -0.015 0.033 -0.085 0.031 -0.007 PACF -0.160 -0.084 -0.100 -0.072 -0.142 -0.083 -0.021 -0.128 -0.038 -0.055 95% C.L. 0.168 0.172 0.173 0.174 0.174 0.175 0.175 0.176 0.177 0.177 |------------------ RESIDUAL CHRONOLOGY AUTOREGRESSIVE MODEL ------------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 1 0.033 -0.160 |---------- REWHITENED CHRONOLOGY AUTO AND PARTIAL AUTOCORRELATIONS -----------| LAG T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 ACF -0.005 -0.006 -0.015 -0.013 -0.027 -0.013 -0.038 -0.039 -0.055 -0.072 PACF -0.005 -0.006 -0.015 -0.014 -0.027 -0.014 -0.039 -0.041 -0.058 -0.077 95% C.L. 0.168 0.168 0.168 0.168 0.168 0.168 0.168 0.168 0.169 0.169 |----------------- REWHITENED CHRONOLOGY AUTOREGRESSIVE MODEL -----------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 8 0.008 -0.008 -0.009 -0.018 -0.016 -0.029 -0.015 -0.040 -0.042 |========================= ARSTAN CHRONOLOGY STATISTICS =======================| |----------------- ROBUST MEAN ARSTAN CHRONOLOGY STATISTICS -------------------| FIRST LAST TOTAL MEAN STDRD SKEW KURTOSIS MEAN SERIAL YEAR YEAR YEARS INDEX DEV COEFF COEFF SENS CORR 1834 1975 142 0.991 0.198 -0.371 3.823 0.225 -0.012 |------------ ARSTAN CHRONOLOGY AUTO AND PARTIAL AUTOCORRELATIONS -------------| LAG T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 ACF -0.012 0.079 -0.088 -0.179 -0.035 -0.085 0.082 -0.252 -0.002 -0.081 PACF -0.012 0.079 -0.087 -0.189 -0.027 -0.066 0.054 -0.292 -0.053 -0.072 95% C.L. 0.168 0.168 0.169 0.170 0.175 0.176 0.177 0.178 0.188 0.188 |------------------- ARSTAN CHRONOLOGY AUTOREGRESSIVE MODEL -------------------| ORD RSQ T-1 T-2 T-3 T-4 T-5 T-6 T-7 T-8 T-9 T-10 0 0.000 |================ AS JIM MORRISON WOULD SAY, "THIS IS THE END" ================| ELAPSED TIME OF TURBO ARSTAN RUN: 0.16 MINUTES